2000/10/31 by Varghese Mathai
Mathematics · #math.DG #msc:19K56 #msc:46L80 #msc:46L87
published as Tohoku Math. Publ., 20 (2001) 107-124 · Latex2e, 16 pages, final version, to appear in a special issue of Tohoku Math. J. (in press)
arxiv created 2001/05/06 · arxiv updated 2009/11/30
In an earlier paper, we established a natural connection between the Baum-Connes conjecture and noncommutative Bloch theory, viz. the spectral theory of projectively periodic elliptic operators on covering spaces. We elaborate on this connection here and provide significant evidence for a fundamental conjecture in noncommutative Bloch theory on the non-existence of Cantor set type spectrum. This is accomplished by establishing an explicit lower bound for the Kadison constant of twisted group C*-algebras in a large number of cases, whenever the multiplier is rational.